Which of the following numbers is a factor of 114? ${4,6,9,12,13}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $114$ by each of our answer choices. $114 \div 4 = 28\text{ R }2$ $114 \div 6 = 19$ $114 \div 9 = 12\text{ R }6$ $114 \div 12 = 9\text{ R }6$ $114 \div 13 = 8\text{ R }10$ The only answer choice that divides into $114$ with no remainder is $6$ $ 19$ $6$ $114$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $6$ are contained within the prime factors of $114$ $114 = 2\times3\times19 6 = 2\times3$ Therefore the only factor of $114$ out of our choices is $6$. We can say that $114$ is divisible by $6$.